ENGINEERING STRUCTURES 137 



prove that such action does not occur. The indicator or water 

 column adopted as a measuring device is a system capable 

 of vibrating naturally with a frequency n per second. If to 

 this system is applied a steady force, or a periodic force whose 

 frequency is much less than n, the actual and recorded 

 pressures are sensibly identical. If, however, the applied 

 force is periodic, and if its frequency 'q ' is much greater than 

 ' n, 9 the maximum displacement of the indicating system 

 will be much less than that corresponding to the actual 

 maximum pressure. Where water-hammer is set up by the 

 sudden stoppage of motion in an enclosed column of water, 

 pressure waves alternately positive and negative in sign are 

 reflected from end to end of the pipe and the disturbance is 

 periodic with a period depending on the length of time required 

 for such a wave to traverse the pipe. If L is the length of the 

 column in feet, the period of a complete cycle of pressure is 

 4L -r V f seconds, where V p9 the velocity of propogation of 

 pressure waves through water is normally about 4700 f.s. 

 It is evident that with such an apparatus as was used in 

 the authors' experiments and in those previously mentioned, 

 the length of the moving column which is brought to rest on 

 impact is almost infinitely small and would be zero but for 

 the compressibility of the water. Any pressure vibration 

 which might be produced would have a frequency almost 

 infinitely great, and could have no perceptible effect on the 

 comparatively slowly vibrating mechanism of the indicator. 



Under such circumstances, the impossibility of obtaining 

 any indication of water-hammer action is sufficiently obvious. 



With a view of increasing the period of any such oscillation 

 of pressure and of enabling it to be recorded, if produced, a 

 coil or zigzag of 1J ins. wrought-iron pipe, having a total 

 length of 100 feet (Fig. 2), was next built up. The upper 

 end of this was open and the lower end was provided with a 

 tee-piece carrying a steam-engine indicator, and terminated 

 in a 1-inch valve V through which water could be admitted 



